"We have ashamed and defeated the attackers," Kenyatta said, adding that "our losses are immense."

The president said five terrorists had been killed "with gunfire" and that 11 others were in police custody. He said 61 civilians were dead and that six law enforcement officers "had made the ultimate sacrifice in their line of duty."

In addition, about 200 people were injured in the siege that began Saturday. Kenyatta said three floors of the mall had collapsed and that several bodies - including those of terrorists and civilians - were buried in the debris.

"It is certainly known that there are more casualties," Kenyan Red Cross spokesman Abbas Gullet told the Associated Press.

Kenyatta said the process of identifying the terrorists was continuing.

"These cowards will meet justice, as will their accomplices and patrons, wherever they are," he said.

He declared three days of national mourning.

Earlier Tuesday, terrorists allied with the Somali Islamist terrorist group al-Shabab had said they were "still holding their ground" in the mall and had hostages with them. A spokesman for the group said the attack was revenge for Kenya's participation in an African force that pushed the group out of the Somali capital of Mogadishu in 2011.

Kenya's Interior Minister Joseph Ole Lenku said the evacuation of hostages had gone "very, very well."

THE DEAD: Kenya's president put the death toll at 72 - 61 civilians, six law enforcement officers and five terrorists. Most of the dead were said to be Kenyans. Also killed: four British citizens, a Dutch woman, two French nationals, an Australian man, a Peruvian, an Indian man and child, a Swiss citizen, a Chinese woman, a South African, a New Zealand man and two Canadians, including a diplomat, their governments said. An African poet and author from Ghana, Kofi Awoonor, also died, Ghana's president said.

Five American citizens were injured, U.S. officials said.

THE ATTACKERS: Kenya Chief of Defense Forces Gen. Julius Karangi said the terrorists are allied with al-Shabab, a Somali group loyal to al-Qaeda that has been fighting for years in Somalia to force it to convert to an Islamist theocracy. Kenya has sent forces to Mogadishu, Somalia, to combat the group.

Kenyan Foreign Minister Amina Mohamed has said "two or three Americans" and "one Brit" were among the attackers. Al-Shabab denied the assertion; the U.S. State Department said it had "no definitive evidence of the nationalities or the identities" of the attackers.

In a Twitter post Tuesday evening, al-Shabab "categorically" denied that women participated in the attack.

"We have an adequate number of young men who are fully committed and we do not employ our sisters in such military operations," the group said.